Hence
the average bet at this level (remember, many of the
bets are zero, when the deck is bad) will be .2377
per cent of $10,000, or $23.77.

To find the average earning i must first determine
how often the deck is favorable. On page 91 i find
the normal curve area to the right of z = .54 is .5000
- .2054 = .2946 which is also the fraction of the
130 card remainders that are favorable to the player.
(Note that the average bet, when one is made, is $23.77/.2946
= $80.69, although this number plays no role in our
calculations.) The average earning will be given by
the formula m
X average perceived advantage + b2 X probability of
favorable deck Plugging in our figures i crank out
an average profit of -.70 X .2377 + (1.28)2 X .2946
= .3163 which is in percent of percent of our bankroll.
Thus our average earning per hand is $.32. Our percentage
advantage on money invested would be .32/23.77 - 1.33%.

What is a trifle unrealistic here is the notion that
the player can diagnose his advantage perfectly. if
a card counting system with betting correlation p
= .96 ire used, i would multiply the original value
of b by p and get a revised b = 1.28 X .96 = 1.23
and repeat the calculations, getting:z
= .70 = .571.23 1770 from page 87 1770 X 1.23 = .21771%),
giving an average bet of $21.77

Area to the right of z = .57 from page 91 is .5000
- .2157 _ .2843
Average earning of -.70 X .2177 + (1.23)z X .2843
= .2777 (% of %), or $.28 with a percentage advantage
on money bet of .28/21.77 = 1.28% Naturally,
to assess total performance throughout the shoe one
would repeat these calculations for various values
of n one expected to encounter, and not just for n
= 130.

Despite
these reasons, lending money in such situations is
fraught with peril. You don't have to be a poker player
to know how many friendships break up over the stresses
that loaned money can create. Regular losers may appreciate
a loan in the moment, but if it helps them lose far
more in an evening than they originally were prepared
to lose, they may be unhappy the next day ("Why
did you lend me money when I was throwing it away
so foolishly?!?"). Someone who loses a truly
huge sum may decide he can't pay it back and quit
the game owing it all. Watching someone use money
you lent him to come back and beat you is almost as
bad.